2.1: Number Talk: Division
Find each quotient mentally.
$5\div\frac13$
$2\div\frac13$
$\frac12\div\frac13$
$2\frac12\div\frac13$
Let’s calculate some rates with fractions.
Find each quotient mentally.
$5\div\frac13$
$2\div\frac13$
$\frac12\div\frac13$
$2\frac12\div\frac13$
A train is traveling at a constant speed and goes 7.5 kilometers in 6 minutes. At that rate:
Freight train Copyright Owner: hpgruesen License: Public Domain Via: Pixabay
Lin ran $2 \frac34$ miles in $\frac25$ of an hour. Noah ran $8 \frac23$ miles in $\frac43$ of an hour.
Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?
In real life, the Mona Lisa measures $2 \frac12$ feet by $1 \frac34$ feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.
The applet is here to help you experiment with the situation. (It won't solve the problems for you.) Use the sliders to scale the image and drag the red circle to place it on the book. Measure the side lengths with the Distance or Length tool.
What size should they use for the scaled copy of the Mona Lisa on the notebook cover?
What is the scale factor from the real painting to its copy on the notebook cover?
Discuss your thinking with your partner. Did you use the same scale factor? If not, is one more reasonable than the other?
There are 12 inches in a foot, so we can say that for every 1 foot, there are 12 inches, or the ratio of feet to inches is $1:12$. We can find the unit rates by dividing the numbers in the ratio:
$1\div 12 = \frac{1}{12}$
so there is $\frac{1}{12}$ foot per inch.
$12 \div 1 = 12$
so there are 12 inches per foot.
The numbers in a ratio can be fractions, and we calculate the unit rates the same way: by dividing the numbers in the ratio. For example, if someone runs $\frac34$ mile in $\frac{11}{2}$ minutes, the ratio of minutes to miles is $\frac{11}{2}:\frac34$.
$ \frac{11}{2} \div \frac34 = \frac{22}{3}$, so the person’s
pace is $\frac{22}{3}$ minutes per mile.
$ \frac34 \div \frac{11}{2} = \frac{3}{22}$, so the person’s
speed is $\frac{3}{22}$ miles per minute.